The inherent precision of the doubly differenced phase measurement and the low cost of instrumentation made GPS the space geodetic technique of choice for regional surveys as soon as the constellation reached acceptable geometry in the area of interest: 1985 in western North America, the early 1990's in most of the world. Instrument and site-related errors for horizontal positioning are usually less than 3 mm, so that the dominant source of error is uncertainty in the reference frame defined by the satellites orbits and the tracking stations used to determine them. Prior to about 1992, when the tracking network for most experiments was globally sparse, the number of fiducial sites or the level at which they could be tied to an SLR or VLBI reference frame usually, set the accuracy limit. Recently, with a global network of over 30 stations, the limit is set more often by deficiencies in models for non-gravitational forces acting on the satellites. For regional networks in the northern hemisphere, reference frame errors are currently about 3 parts per billion (ppb) in horizontal position, allowing centimeter-level accuracies over intercontinental distances and less than 1 mm for a 100 km baseline. The accuracy of GPS measurements for monitoring height variations is generally 2-3 times worse than for horizontal motions. As for VLBI, the primary source of error is unmodeled fluctuations in atmospheric water vapor, but both reference frame uncertainties and some instrument errors are more serious for vertical than horizontal measurements. Under good conditions, daily repeatabilities at the level of 10 mm rms were achieved. This paper will summarize the current accuracy of GPS measurements and their implication for the use of SLR to study regional kinematics

King, Robert W.

English

NASA Technical Reports Server

N95- 14279
EB GLOBAL AND REGIONAL KINEMATICS WITH GPS
R.W. King
INTRODUCTION
The inherent precision of the doubly differenced phase measure-
ment and the low cost of instrumentation made GPS the space
geodetic technique of choice for regional surveys as soon as the
constellation reached acceptable geometry in the area of
interest: 1985 in western North America, the early 1990s in most
of the world. Instrument and site-related errors for horizontal
positioning are usually less than 3 mm, so that the dominant
source of error is uncertainty in the reference frame defined by
the satellites orbits and the tracking stations used to determine
them. Prior to about 1992, when the tracking network for most
experiments was globally sparse, the number of fiducial sites or
the level at which they could be tied to an SLR or VLBI reference
frame usually set the accuracy limit [e.g., Feigl et al., 1993].
More recently, with a global network of over 30 stations, the
limit is set more often by deficiencies in our models for non-
gravitational forces acting on the satellites. For regional
networks in the northern hemisphere, reference frame errors (or
uncertainties) are currently about 3 parts per billion (ppb) in
horizontal position, allowing centimeter-level accuracies over
intercontinental distances (Figure I) and less than 1 mm for a
i00 km baseline (Figure 2).
The accuracy of GPS measurements for monitoring height variations
is generally 2-3 times worse than for horizontal motions. As for
VLBI, the primary source of error is unmodeled fluctuations in
atmospheric water vapor, but both reference frame uncertainties
and some instrumental errors are more serious for vertical than
horizontal measurements. Under good conditions, daily repeat-
abilities at the level of i0 mm rms have been achieved (Figure
3), leading to the hope that with frequent or continuous measure-
ments, long-term monitoring of geophysical changes in station
heights can be accomplished at the millimeter level.
This paper will attempt to summarize the current accuracy of GPS
measurements and their implication for the use of SLR to study
regional kinematics. Readers not familiar with the fundamentals
of GPS surveying, both field work and analysis, are referred to
the recent reviews by Dixon [1991], King and Blewitt [1990], and
Hager et al. [1991].
NON-ORBITAL ERRORS IN POSITIONING
There are four primary sources of GPS measurement error that are
not related to the accuracy or stability of the reference frame:
i) operator setup error; 2) signal multipathing; 3) deficiencies
in modeling the atmosphere; and 4) error or uncertainty in
relating the effective phase center of the antenna to the ground
47
https://ntrs.nasa.gov/search.jsp?R=19950007865 2020-06-16T10:15:09+00:00Z
mark. For horizontal measurements, each of these sources usually
contributes between about 0.5 and 2 mm, so that the aggregate
effect varies between 1 mm and 5 mm, with 2-3 mm typical. For
vertical measurements, atmospheric effects dominate, at 10-50 mm,
except on very short (<2 km) baselines.
Operator setup errors can be limited to about 1 mm in both
horizontal and vertical with sufficient care by the field
operator. Miscalibrated tribrachs, poor lighting, high wind, and
poorly defined center points on the ground monuments can degrade
the quality of the setup, but it would be unusual for the total
error to exceed 2 mm. For permanent sites with antennas
mechanically fixed to a ground mark, there is no significant
setup error contributing to measurements of the change in
position.
Multipath errors are strongly dependent on the environment of the
site and the type of antenna used. They are also among the most
difficult to assess since they tend to repeat from day to day and
alias with atmospheric effects for low elevations. Often the most
obvious multipath signature - high amplitude and frequency in the
phase residuals - has minimal effect on position estimates, but
the invisible low-frequency component may be introducing
significant error. I know of no systematic study that quantita-
tively and reliably relates identifiable multipath to errors in
horizontal or vertical position. Crude numerical experiments
carried out at MIT, in which spans of high multipath are deleted
from the analysis and the elevation cutoff varied, suggest that
even several centimeters of high-frequency multipath usually
affects horizontal position estimates at the level of only 1-3
mm. Since multipath is frequency dependent (dispersive), its
effect is amplified when the ionosphere-free linear combination
(LC or L3) of the two GPS signals (LI and L2 ) is formed; thus, it
will introduce less error into the measurement of very short (<5
km) baselines for which the L 1 (and/or L2) signal can be used
directly.
Atm0spheric errors are most serious in estimates Of vertical
position but can affect estimates of the horizontal if there are
azimuthal asymmetries in either the atmospheric delay or the
geometry of the satellite constellation. As for VLBI, both water-
vapor radiometer measurements and stochastic estimation
techniques have proven successful in improving estimates of
vertical position [Tralli and Lichten, 1990], but the low
elevation (<15 degrees) observations used with fixed VLBI
antennas to separate atmospheric and height parameters are not as
effective since GPS antennas are omnidirectional and thus subject
to significant signal multipathing. To the advantage of GPS,
however, are the larger number of "sources" to be observed and
the low cost of frequent measurements. Since atmospheric errors
for many (though not all) sites are nearly random, the accuracy
can be improved by averaging over a large number of observations.
This strategy is most easily followed with permanent tracking
48
sites, which can observe continuously for months or years [Bock
and Shimada, 1990].
The phase centers of all commonly used GPS antennas have
elevation-dependent variations of i0 mm in the LC observable, and
some are as large as 50 mm. These variations cancel when matched
antennas are used over regional baselines, for which the
elevation angle of the satellites from both sites is nearly the
same. Alternatively, they can be modeled using anechoic chamber
measurements of the antennas [Schupler et al., 1992]. The most
serious problem occurs when antennas of different types are used
in a survey [Braun et al., 1993; Mireault et al., 1993]. For the
commonly used combination of Rogue (Dorne-Margolin with JPL choke
ring) and Trimble antennas, horizontal errors of about 2 mm and
vertical errors of about 4 mm remain even after modeling the
variations [S. McClusky, personal communication, 1994]. Modeling
also becomes more important for long baselines since the
elevation angle of the satellites will be different for each
station. For example, introducing a phase-center model to our
analysis of 23 global sites with matched Rogue antennas from the
1991 "GIG" experiment changed estimated heights by 20-30 mm.
STABILITY OF THE GLOBAL REFERENCEFRAMEFOR REGIONAL SURVEYS
With the current (43-station) tracking network of the Inter-
national GPS Geodynamics Service (IGS) there may still be non-
negligible reference-frame (baseline-length dependent) errors for
regional surveys. The dense northern hemisphere network provides
reference-frame control at the level of 1-4 ppb for horizontal,
and 2-8 ppb for vertical positions [Blewitt et al., 1992; Heflin
et al., 1992]. For the southern hemisphere, however, the density
of tracking stations may not be sufficient to reach this level of
stability. Analysis of the 1991 GIG experiment, which included 5
southern hemisphere stations, resulted in repeatabilities of 5-10
ppb for baselines between northern and southern hemisphere
stations, and 15 ppb for southern hemisphere baselines [Heflin et
al., 1992]. The current IGS network includes nine southern
hemisphere sites (soon to expand by another five), and there is
clear evidence that the stability of the reference frame has
shown marked improvement [Heflin et al., 1993].
Although the GPS orbits are dynamically tied to the Earth's
center of mass, their high altitude and perturbations by non-
gravitational forces result in a significantly weaker tie than
for lower laser geodetic satellites such as Lageos. While SLR
currently provides a determination of the center of mass at the
level of about one centimeter for monthly averages, the GPS
estimate is no better than a decimeter [M.G. Heflin and T.A.
Herring, personal communications, 1994]. By constraining the
motion of the center of mass, however, a few ppb stability can be
achieved without applying any further constraint in position or
velocity from SLR or VLBI measurements.
49
SUMMARYAND IMPLICATIONS FOR SLR RESOURCES
For densification of regional networks less than i000 km in
extent, there is little question that GPS measurements equal or
exceed the horizontal accuracy available from mobile VLBI or SLR
and at a fraction of the cost. For large-scale regional and
global kinematics, GPS seems poised also to supplant the_Qlder
techniques, due principally to the relative economy of fixed,
continuously tracking stations. There are some regions of the
world for which the longer span of SLR plate motion measurements
may warrant their continuation at one or two sites for a few more
years [see, e.g., Oral, 1994]. These measurements are most
valuable if they provide velocity constraints for the region at
the level of a few mm/year.
The jury is still out on the ultimate accuracy and role of GPS in
monitoring height variations. Like SLR and (at least mobile)
VLBI, GPS seems stuck at the i0 mm level, which may not be
sufficient for studying vertical tectonic motions and changes in
global sea level. Among the most important experiments that can
be carried out over the next few years are rigorous
intercomparison of vertical measurements using the three
techniques together with efforts to improve the accuracy of each.
ACKNOWLEDGEMENTS
I am grateful to Geoff Blewitt, Yehuda Bock, Mike Heflin, Tom
Herring, Chopo Ma, Peter Morgan, Burc Oral, and Paul Tregoning
both for discussions and the use of figures for the presentation
leading to this written summary.
REFERENCES
Blewitt, G., M.B. Heflin, F.H. Webb, U.J. Lindqwister, and R.P.
Malla, Global coordinates with centimeter accuracy in the
International Terrestrial Frame using GPS, Geophys.Res.Lett., 19,
853-856, 1992.
Bock, Y., and S. Shimada, Continuously monitoring GPS for
deformation networks, in Global Positioning System: An Overview,
IAG Symp. No. 102, Y. Bock and N. Leppard, eds., Springer-Verlag,
New York, 1990.
Bock, Y., Permanent GPS Geodetic Array: Continuous measurement
of active tectonics in S. California, (abstract) , EOS, Fall
Meeting Suppl., 43-59, 1993.
Dixon, T. H., An introduction to the Global Positioning System
and some tectonic applications, Rev. Geophys., 1991.
Braun,J., C. Rocken, and C.M. Meertens, GPS antenna mixing and
phase center corrections (Abstract), EOS Full Meeting Suppl., 74,
197, 1993.
5O
Feigl, K.L., D.C. Agnew, Y. Bock, D. Dong, A. Donnellan, B.H.
Hager, T.A. Herring, D.D. Jackson, T.H. Jordan, R.W. King, S.
Larsen, K.M. Larson, M.H. Murry, Z. Shen, and F.H. Webb, Space
geodetic measurement of crustal deformation in central and
southern california, 1984-1992, j.Geophy.Res., 98, 21677-21712,
1993.
Hager, B.H., R.W. King, and M.H. Murray, Measurement of crustal
deformation using the global positioning system, Ann. Rev. Earth
Planet. sci., 19, 351-382, 1991.
Heflln, M., W. Bertiger, G. Blewitt, A. Freedman, K. Hurst, S.
Lichten, U. Lindqwister, Y- Vigue, F. Webb, T. Yunck, and J.
Zumberge, Global geodesy using GPS without fiducial sites.,
Geophys.Res.Lett., 19, 131-134, 1992.
Heflin, M., G. Blewitt, D. jefferson, Y- vigue, F. Webb, D.
Argus, T. Clark, J. Gipson, and C. Ma, Global positions and
velocities from one year of GPS data, viewgraphs from paper
presented at the 1993 Fall Meeting of the AGU, EOS, 93, 194,
1993.
King, R.W., and G. Blewitt, Present capabilities of GPS for high-
precision regional surveys, in Global Positioning System: An
overview, IAG Symp. No. 102, Y. Bock and N. Leppard, eds.,
springer-Verlag, New York, 1990.
Mireault, Y-, F. Lahaye, and P. Taylor, Preliminary investigation
of inter-receiver biases between Ashtech, Leica, Rogue, and
Trimble GPS receivers, viewgraphs from paper presented at the
1993 Fall Meeting of the AGU, EOS, 93, 197, 1993.
Oral, M.B., Global Positioning System measurements in Turkey
(1988-1992), Kinematics of the Africa-Arabia-Eurasia plate
collision zone, Ph.D. Thesis, MIT, Cambridge, MA, 343pp, 1994.
Schupler, B.R., R. Allshouse, and T. Clark, GPS antennas -
measurements and multipath, DOSE Investigator Working Group
Meeting, October, 1992.
Tralli, D.M., and S.M. Lichten, Stochastic estimation of
tropospheric path delays in Global Positioning System geodetic
measurements, Bull. Geod. 64, 127-159, 1990.
51
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Figure 1. Time evolution of the north, east, and height of Algonquin from GPS estimates
in GIG '91 and 1992-93 [Heflin et al., 1993]. The reference frame is defined solely by
the global network of GPS tracking stations.
52
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day number, 1993
Figure 2. Daily baseline estimates for the relative position of PGGA sites at Lake Mathews
(MATH) and Palos Verdes (PVER), June-September, 1993. A comparison of solutions
using simultaneously estimated and extrapolated orbits indicates no significant contribution
of orbital error for this 90-km baseline [Bock, 1993].
53
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Figure 3. Vertical repeatabilities over 3 days for baselines in a 87-station network in
Kazakhstan surveyed in July, 1993. The horizontal gray line gives the average value of the
rms, and the lighter, curved line shows the expected error of first-order leveling. There is a
large amount of (expected) scatter in the rms values since each is based on only 3
determinations. IT. A. Herring, personal communication, 1993].
54


Global and regional kinematics with GPS

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